Jobs for a non-US citizen in space companies?

Hey everyone. Lately, I've been searching for space companies that hire engineers (especially mechanical, aerospace engineers). I'm an undergraduate in mechanical engineering, seeking to major in some space-related field in the future. But I want to know what I'm getting myself into, so I want to know the perspectives for a non-US MechE with a major in the aerospace field looking for a job abroad.
Yeah, I do know some of the most famous aerospace companies: Airbus/Boeing/Lockheed Martin... Of these, I think it's airbus that interests me the most. I would love to work with rocket propulsion, for example. I've came across with this Planetary Resources too, but I don't know much about them, except it's something about asteroid mining.
So, for a non-US and non-European citizien, what are the chances of working at one of these companies? I mean, how is the market now and what are the prospects for the near future(like 5-10 years from now?).
And if you know any other space-related company, could you list them here please?

Thanks for your responses, but there's something more I would like to know. First of all, I've seen that ITAR will be a big problem for me in the future if I'm seeking to get a job in the aerospace industry in US. I trust that, aside from aerospace, there are other engineering sectors more open to non-US citiziens so I can progress with my career, slowly making my way to companies like Boeing.
Does the rules of ITAR applies to interns too? I think that getting an internship at some aerospace companies could help, especially in my curriculum.

Even so, I think it will be difficult to get a work visa for an internship. I don't know how temporary work visas work in the US and Europe. Would it be reasonable to pursue one for an undergraduate internship program?

That isn't a problem. Where I work (government research facility) we hire international interns all the time, it is quite commonplace. We don't hire them for ITAR sensitive projects but the majority of groups have projects available that are fair game. Over the last several years my group has hired interns from Brazil, South Korea, Germany, UK, Switzerland, and Columbia (as well as the US, of course)

I prefer to remain (mostly) anonymous. I can tell you that we get our interns from specific groups at partner universities. Also my group hires EE students. Other groups are ME focused but I don't work with them typically. What university do you attend in Brazil?

And one more thing: if I eventually get a green card, can I then work on ITAR projects? I've heard about some people that managed to get a major in the US and, while there, found some non-ITAR related companies to sponsor their work visa and then climbed up to apply for a green card. I really don't know how those things work, so I would gladly thank any advice. I've just stumbled upon ITAR and it was a big
disappointment for me, since my dream job is working at aerospace in a big company like Boeing or SpaceX.
So my question is: if I find some company to sponsor my work visa on a non-ITAR related project, can I make my way up to become a US person later?

I want to interject because I think you are starting to get the wrong ideas here.

1. Many, if not most, of the REGULAR undergraduate "internships" at US National Labs and US universities are only open to students from US institutions. That is important to take note of. In a lot of cases, they are for US citizens and permanent residents, but there are internships programs that are opened to international students at US institutions.

2. Unless your home universities have agreements, partnerships, etc. with institutions here in the US, of if there is a special exchange program, then your internships opportunities here in the US is severely limited.

3. US companies have limited ability to hire non-US citizens, i.e. they just can't hire as many as they like. Most US companies will NOT hire non-permanent resident or non-citizens. Those who do will tend to first hire non-citizens on a temporary basis using the H1 visa status, and even this is limited since the US govt. allows only a certain number of H1 visas per year. And again, this is temporary. You can have, at most, 6 years working under this visa before you have to leave the country.

4. If that company that gave you the temporary visa likes you and wants you permanently, then they will have to abide by US labor laws and justify your hiring. Only then will you have the opportunity to apply for permanent resident status, which is another long and tedious process depending on the applicable permanent resident category.

The fact that you are not in a US institution currently makes it more difficult to get into all those institutions that you already talked about.

The fact that you are not in a US institution currently makes it more difficult to get into all those institutions that you already talked about.

I plan to do my master's degree in the US, and while I'm there, look if I can get any company to apply for a work visa for me. It's that hard for companies hiring non-US even if they are non-ITAR related? Well, that's sad.

So, aerospace in the US for a non-US is virtually unachievable? Do you know anything about this industry in Europe? It's so hard as in the US or would I have more possibilities there?

If you go to a US university for your MS degree you should have no trouble finding an internship or work at a US company. In my graduate group 3/4 of the students were non-US persons.

That's good to know. But if I get there to study will be on a students visa, yes? And if I am to find work there, my employer would have to apply for a work visa to me, am I right? I think that the complicated business is right over there, finding someone who will deal with all the paperwork involved. And as ZapperZ said, even that will be on a temporary basis, with a limited number of H1 visas per year.

The H1 program is for career positions where the company supposedly can't find a US person to fill the role. They can sometimes be tricky to get but if you are known to a company and they want you they can usually keep you. For students you would use a J1 which are much easier to get. I've never heard of a graduate student not being able to get a visa for job. I've also only heard of one person graduating from a US school having to return to his home country not by choice (because he could not find a job). This was in 2009 during our last recession.